Nonparametric Estimation of the Conditional Mode with Errors-In-Variables: Strong Consistency for Mixing Processes
Authors:
D. A. Ioannides a;
E. Matzner-L
ber b
ber b
| Affiliations: | a Department of Economics, University of Macedonia, 54006 Thessaloniki, Greece. |
b Laboratoire de Statistique, Universit de Rennes II, 35043 Rennes, France. |
DOI:
10.1080/10485250212375
Publication Frequency:
8 issues per year
Subjects:
Mathematical Economics;
Mathematical Finance;
Medical Statistics;
Statistical Theory & Methods;
Statistics;
Statistics for the Biological Sciences;
Stochastic Models & Processes;
Number of References: 13
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Abstract
Having two variables, an explanatory one ( X o ) and a response one ( Y o ), linked by the classical relation Y^
o = g( \bf X ^ o ) + \varepsilon , we want to estimate the function g (.) without any parametric assumption. However, in a lot of situations, the variables are not measured directly but through their proxies \bf X = \bf X ^ o + \bivarepsilon and Y = Y^ o + \eta where and -are the measurements errors. We propose here a new method for estimating the function g (.) in such a context. Our estimator is based on deconvoluted kernels. Uniform convergence is established for strongly mixing stochastic processes. Some simulations show that our estimator is tractable and performs relatively well in practice.
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Keywords:
Deconvolution;
Measurement Errors;
Nonparametric Estimation;
Conditional Density And Mode;
Uniform Consistency;
-mixing
|
| view references (13) : view citations |

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de Rennes II, 35043 Rennes, France.
o
= g(
and -are the measurements errors. We propose here a new method for estimating the function g (.) in such a context. Our estimator is based on deconvoluted kernels. Uniform convergence is established for strongly mixing stochastic processes. Some simulations show that our estimator is tractable and performs relatively well in practice.
-mixing
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